Percent Calculator

Percentage calculator for six common problems

Select the wording that matches your question. The calculator can find a percentage of a number, express one value as a percentage of another, recover the whole from a known part and percentage, calculate percent change, calculate percentage difference, or increase and decrease a number by a percentage.

What is X% of Y?

Convert the percentage to a decimal and multiply it by the value. For example, 20% of 150 is 0.20 x 150 = 30.

part = percentage / 100 x whole

X is what percent of Y?

Divide the part by the whole and multiply by 100. For example, 30 is 20% of 150.

percentage = part / whole x 100

Convert a ratio to a percentage

First identify the denominator. With 2 red counters and 3 blue counters, red is 2/5 of all counters, or 40%, while red compared only with blue is 2/3, or about 66.6667%. Choose X is what percent of Y and enter X = 2, Y = 5 for the share of the whole. Using Y = 3 answers the part-to-part question instead.

For simplifying two- or three-part ratios and dividing an amount into shares, use the ratio calculator. To reduce a fraction or convert a terminating decimal exactly, use the fraction calculator. OpenStax's introduction to percent explains the connection between fractions, decimals and percentages.

X is Y% of what?

Divide the known part by the percentage written as a decimal. If 30 is 20% of a number, the whole is 30 / 0.20 = 150.

whole = part / (percentage / 100)

Percent change

Percent change compares a new value with its original value. A positive result is an increase and a negative result is a decrease. Moving from 100 to 125 is a 25% increase.

percent change = (new - original) / |original| x 100

Percentage difference

Percentage difference compares two values without treating either one as the original baseline. It divides the absolute difference by the average magnitude. The values 80 and 120 have a 40% percentage difference.

percentage difference = |value 1 - value 2| / ((|value 1| + |value 2|) / 2) x 100

Percentage points are different

If a rate rises from 20% to 25%, it increases by 5 percentage points but by 25% relative to its original level. Use percentage points when subtracting two percentages directly; use percent change when comparing the relative movement.

Frequently asked questions

How do I calculate a 15% increase?

Multiply the starting value by 1.15. A 15% increase on 200 gives 230.

How do I calculate a 15% decrease?

Multiply the starting value by 0.85. A 15% decrease on 200 gives 170.

Why can percent change be undefined?

The formula divides by the original value, so a change from zero has no finite percentage. Use the absolute change instead.